Assessing the Variation of Formal Military Alliances

Article

Assessing the Variation ofFormal Military Alliances

Brett V. Benson1 and Joshua D. Clinton1

AbstractMany critical questions involving the causes and consequences of formal militaryalliances are related to differences between various alliances in terms of the scopeof the formal obligations, the depth of the commitment between signatories, andthe potential military capacity of the alliance. Studying the causes and conse-quences of such variation is difficult because while we possess many indicators ofvarious features of an alliance agreement that are thought to be related to thebroader theoretical concepts of interest, it is unclear how to use the multitude ofobservable measures to characterize these broader underlying concepts. Weshow how a Bayesian measurement model can be used to provide parsimoniousestimates of the scope, depth, and potential military capacity of formal militaryalliances signed between 1816 and 2000. We use the resulting estimates to exploresome core intuitions that were previously difficult to verify regarding the forma-tion of the formal alliance agreement, and we check the validity of the measuresagainst known cases in alliances as well as by exploring common expectationsregarding historical alliances.

Keywordsalliance, international alliance, international treaties, military alliance, measurement,treaty design

1Department of Political Science, Vanderbilt University, Nashville, TN, USA

Corresponding Author:

Brett V. Benson, Department of Political Science, Vanderbilt University, PMB 505, 230 Appleton Place,

Nashville, TN 37203, USA.

Email: [email protected]

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Understanding the formation and consequences of formal military alliances is a

research program that is central to the study of international relations. Military alli-

ances help define and shape the nature of interactions between countries, and by

structuring international obligations, they help construct the nature of the interna-

tional system. Better understanding not only the ways in which formal alliances

vary but also why this variation occurs is critically important for understanding

interstate relations. So too, of course, is the importance of exploring their actual

impact on international behavior.

Formal military alliances differ a great deal. Consider, for example, the differ-

ences between the 1920 Franco-Belgian agreement and the 1915 multilateral alli-

ance among France, Russia, United Kingdom, and Italy. Both contain defensive

obligations, include France as an alliance member, target a specific adversary,

and are signed in approximately the same time period. Beyond these similarities,

the agreements differ a great deal. In addition to specifying precisely the amount

of troops to be committed under certain conflict scenarios, the Franco-Belgian

agreement publicly requires both sides to organize a system of defense including

the merging of their military forces, the joint occupation of the Rhineland, and

mutual assistance in the provision of war materiel. By contrast, the 1915 multilat-

eral agreement was signed in secret during wartime and contains offensive and

consultation obligations. Yet, the formal terms of the 1915 agreement do not spe-

cifically describe costs required of the signatories to organize and integrate their

militaries.

How should we compare these two alliances? On one hand, the 1915 agreement

obligates alliance members to take military action under a greater set of circum-

stances, because it contains commitments of military intervention under both offen-

sive and defensive conditions. It also involves several relatively powerful countries

as signatories. On the other hand, the 1920 Franco-Belgian accord requires alliance

members to pay high costs to form the commitment by stipulating that both sides

will actively integrate their militaries, jointly base their troops, and mutually develop

and provide war materiel. Moreover, the agreement is a public declaration that may

entail some reputation costs if alliance obligations are not kept. With so many points

of difference, examining these two alliances together seems, in many ways, to be an

apples-to-oranges comparison. Is there a straightforward way to compare various

characteristics of formal military alliances that will help us begin to study the rea-

sons for, and the implications of, core distinctions?

We focus on two motivating questions: First, can we use observable features of

formal alliance agreements and characteristics of the signatories themselves to pro-

vide a more parsimonious characterization of the extent to which alliances differ

from one another? Second, can we explore the variation to help us better understand

the politics of alliance formation? Better understanding the willingness of signa-

tories to enter into different types of alliances depending on their situation and that

of their fellow signatories is important for understanding the construction of the

international arena.

Benson and Clinton 867



Our approach begins with the observation that formal military alliances vary in

coherent ways. Alliances vary in the breadth of the circumstances to which the

obligations of a military alliance have application (hereafter scope) as well as the

costliness of the obligations to which signatories commit themselves when they

join the alliance (hereafter depth). Agreements with sweeping offensive and defen-

sive provisions, for example, are obviously broader in the scope of the military

obligations contained in the terms of the agreement than neutrality pacts. Defen-

sive commitments that formalize joint military planning as well as requirements

for peacetime military integration, the provision of aid, and military basing impose

deeper costs on the alliance members than agreements that only contain defensive

obligations. Alliances also vary in terms of their pooled military strength (hereafter

potential military capacity)—multiple powerful and ideologically aligned major

powers likely have more potential military capacity than a bilateral alliance

between minor powers with divergent preferences.

Identifying the range of alliances that exist and probing the conditions under

which various types of alliances are likely to be formed along the dimensions of

scope, depth, and potential military capacity of formal military alliances is key to

understanding the role of military alliances in structuring the international system.

Scholars have emphasized the importance of these concepts for characterizing and

understanding the formation and consequences of military alliances (see Snyder

1997; Leeds et al. 2002; Schelling 1966; Benson 2011, 2012; and especially Leeds

and Anac 2005). Research on these topics would benefit from a single parsimonious

measure of each concept, but an empirical characterization remains elusive in spite

of a wealth of data. The difficulty is due to the multifaceted aspect of these alliance

features, which requires that any characterization is best inferred from multiple

observable attributes.

We use a statistical measurement model to provide a principled framework for

estimating the scope, depth, and military capacity of formal military alliances. Meth-

odologically, our approach is similar to the approach taken by scholars interested in

measuring the ideology of elected and unelected officials (e.g., Poole and Rosenthal

1997; Martin and Quinn 2002; Clinton, Jackman, and Rivers 2004), the positions of

a political party in an underlying policy space (Budge et al. 2001), the ideology of a

congressional district in the United States (Levendusky, Pope, and Jackman 2008),

the extent to which a country is democratic (Pemstein, Meserve, and Melton 2010),

the positions taken by a country in the United Nations General Assembly (Voeten

2000), or the depth of preferential trade agreements (Dur et al. 2014).

Our approach makes several contributions. First, we show how a Bayesian

latent trait model (Quinn 2004) can recover a theoretically informed, multidimen-

sional estimate of alliance variation that reflects the scope, depth, and potential

military capacity of formal military alliances while also quantifying the sometimes-

substantial uncertainty that we have about the resulting estimates (Jackman 2009b).

We also demonstrate how the resulting measures quantify the influence of various fea-

tures and allow us to discriminate between alliances belonging to broad classifications

868 Journal of Conflict Resolution 60(5)



that previous scholarship has been unable to disentangle when relying on particular

observable alliance features (e.g., having to equate ‘‘offensive alliances’’ with more

a expansive scope of commitment).

In validating our measures using both qualitative and quantitative information,

we are also able to validate several important substantive conclusions regarding

the politics of alliance formation. We demonstrate that notions regarding the

scope, depth, and potential military capacity of a military alliance are distinct and

meaningful measures. We also highlight that our measures of notable alliances

comport well with the existing expectations, and we show how prominent alliances

within a theater of operations show evidence of ‘‘balancing’’ in terms of both the

potential military capacity of the signatories involved and the scope and depth of

the formal treaty commitments.

We also find that many, but certainly not all, of the alliances that are exceptional

in one respect are less so in others. This suggests that there are likely meaningful

trade-offs associated with designing deeper and broader alliance agreements. For

example, relatively weak signatories may occasionally wish to strengthen their alli-

ance through deeper treaty terms that are designed to expand their combined capabil-

ities through costly peacetime military coordination and sweeping wartime

obligations, but militarily powerful alliance signatories may wish to curtail allies’

access to the aggregate capabilities of the alliance by designing conditions that limit

military intervention or make it costless to escape.

Finally, we use our measures to analyze the formation conditions of formal mil-

itary alliances. That is, we examine whether factors that are predicted to affect the

scope and depth of alliances when they are initially formed covary as expected. Our

analysis not only helps confirm the validity of the measures that we recover but also

contributes to our understanding of alliance formation. Whereas existing empirical

work is often forced to deal with many coarse, but relevant alliance features, the

measurement model we present summarizes the information contained in the multi-

ple measures and, in so doing, provide a more nuanced characterization of the way in

which alliance agreements vary.

Conceptualizing Variation in Alliances

A natural starting point for conceptualizing how formal military alliances vary

involves considering the formal terms of the agreement and the characteristics of the

signatories involved. Each of these, however, consists of many different factors and

a wealth of available data. Our goal is to integrate the many measures that have been

collected in a principled way so as to provide a meaningful characterization of alli-

ance agreements that reflects variation along conceptually distinct dimensions. We

focus on the following three dimensions: scope of the obligations, depth of commit-

ment, and potential military capacity. Scope accounts for the variation in the breadth

of the circumstances under which the terms of the agreement obligate alliance mem-

bers to commit military action. Depth reflects the degree to which the alliance




agreement imposes peacetime and related costs on the signatories. Potential military

capacity measures the total adjusted potential military power or strength of using

characteristics of alliance members.

These three concepts are important for many fundamental questions related to

military alliances. The scope of the obligations contained in alliance agreements

is related to questions on the formation of military alliances. Scholars, for example,

have argued that alliance members have incentives to limit their obligations when

there are entrapment concerns (Snyder 1984, 1997; Fearon 1997; Zagare and

Kilgour 2003; Kim 2011; Benson 2012). The depth of alliance commitments is also

relevant for alliance formation, and some argue that incentives for opportunism may

lead to deeper agreements (Leeds and Anac 2005; Abbott and Snidal 2000; Lake

1999). For example, Snyder (1997, 11) points out that states often include costly

actions in their alliance commitments to ‘‘validate’’ agreements ‘‘when interests

of allies are somewhat divergent, or when they are subject to change. . . . ’’ Accord-

ing to Snyder, when signatories’ preferences diverge, ‘‘The partner will need to be

reassured that one’s underlying interests are not so at odds with the contract that the

alliance is no more than a ‘scrap of paper.’’’ In general, scholars believe that alli-

ances entail deeper commitments to incur peacetime costs when concerns about

opportunism exist and when signatories may have divergent preferences.

The concepts of scope and depth are also relevant for better understanding the

effects of military alliances. Are agreements containing a broader set of agreed-

upon obligations related to conflict initiation and war? Are deeper alliance agreements

any more credible? If the imposition of costs signals information and facilitates the

coordination of warfighting abilities (Morrow 1994; Fearon 1997), alliances that

impose greater costs during peacetime may be more reliable.

The potential military capacity of an alliance is another critical concept.

Balance of power theories, for example, considers how the distribution of power

resulting from the joint military strength of competing alliance networks affects

the stability of the international system (Morgenthau 1948; Organski 1968; Waltz

1979; Walt 1987), and there is a long debate with an extensive empirical literature

about the effect of alliances in various theories of the distribution of power and sta-

bility.1 Potential military capacity is also relevant for understanding the deterrent

effect of military alliances and whether the combined potential military force of

the allies might affect an adversary’s calculation to challenge one of the allies

(Morrow 1994; Smith 1995; Leeds 2003b; Zagare and Kilgour 2003; Yuen

2009; Johnson and Leeds 2011; Benson 2012; Benson, Meirowitz, and Ramsay

2014; Benson, Bentley, and Ray 2013).

Measuring the Scope of Obligations

Our characterization of scope draws on conventional conceptualizations. Scholars

generally agree that alliance agreements typically specify the primary obligations

of alliance members, some of which require members to become involved militarily




in a broad set of circumstances while others are more limited in scope. For example,

Snyder (1997) explains that offensive alliance agreements obligate alliance mem-

bers in a wide range of circumstances compared to those written to secure a third

party’s neutrality in the case of a military conflict. This is the standard view of

alliances—agreements with offensive and defensive provisions obligate members

to commit military action to a broader range of circumstances than defensive

agreements alone, and defensive agreements are broader in military scope than,

say, consultation pacts or neutrality agreements, which do not bind signatories

to commit militarily to any conflict and may even require states not to become

involved militarily.

Following the Alliance Treaty Obligations and Provisions (ATOP) categoriza-

tion of obligations that commit alliance members to military action or nonaction

(Leeds et al. 2002), we begin by including in our estimation of scope the variables

from the ATOP project that indicate whether an alliance is offensive or defensive.2

The difference between these alliances in the ATOP coding is that offensive provi-

sions obligate at least one member to commit military support in conflicts involving

an alliance member even if the conflicts were not triggered by an attack by a nonal-

liance member on an alliance member. Alliances coded as defensive include provi-

sions that condition military action on an attack by a nonalliance member on an

alliance member. We also include agreements with neutrality and consultation provi-

sions, because such obligations require nonmilitary actions of alliance members. We

do not include agreements that include only nonaggression provisions. These alliances

may be fundamentally different in their design and purpose from those we aim to ana-

lyze (Mattes and Vonnahme 2010). Nonaggression pacts focus on avoiding war

between signatories themselves, whereas the alliances we focus on include provisions

that specify promises of actions related to conflicts with third parties.

In addition to these traditional classifications of alliance agreements, we follow

ATOP rules and include variables indicating whether an alliance contains more spe-

cific conditional provisions. Accordingly, we include the following indicator vari-

ables: military action depends on war environment, nonmilitary action depends on

war environment, military action depends on noncompliance, nonmilitary action

depends on noncompliance, military action depends on nonprovocation, nonmilitary

action depends on nonprovocation, nonmilitary action required only if requested,

and conditional other. The two war environment variables indicate whether military

(in the case of agreements where the primary obligations are offensive or defensive)

or nonmilitary (in the case of agreements where the primary obligations are neutral-

ity or consultation) action is conditional on some factor relating to the war environ-

ment such as a specific adversary, location, ongoing conflict, or number of

adversaries. The two noncompliance variables indicate whether military/nonmilitary

action is conditional on the noncompliance with a certain demand. The two nonpro-

vocation variables indicate whether military/nonmilitary action is conditional on one

of the alliance members being attacked without provocation. The variable nonmili-

tary action required only if requested indicates whether consultation is required only if




requested by an alliance member. The variable conditional other refers to any other

condition specified in the agreement that is not covered by these other variables. Each

of these provisions delineates scope conditions for military action.

We also include the ATOP variables that identify conditions in the agreement for

renouncing the obligations. These variables include renunciation allowed, renuncia-

tion prohibited, and renunciation conditional. Renunciation allowed permits any

alliance member to renounce at any time without advance notice. Renunciation pro-

hibited stipulates that renunciation is strictly prohibited. Renunciation conditional

indicates whether an agreement permits renunciation if another member takes an

aggressive action. Renunciation conditions are critical for informing the conception

of scope, because they stipulate whether the primary obligations for military or

nonmilitary action are firm or flexible. Flexibility of terms may limit the scope.

Comparing two offensive agreements similar in every way except one permits

renunciation and another does not, the more flexible agreement may be more limited

because it allows for the inapplicability of military action conditional on factors that

may be determined by the alliance members on an ad hoc basis.

The scope of the obligations agreed to in an agreement also varies depending on

whether the alliance is designed to deter or to compel. Schelling (1966) distin-

guished between deterrent military commitments that are intended to prevent

changes to the status quo and compellent commitments that are designed to induce

or coerce changes in the status quo. Compellent threats condition military action on

noncompliance with an explicit or implicit demand on the target to make a conces-

sion. Consequently, following Benson (2012), we include a variable indicating

whether an agreement includes a compellent provision. We also use Benson’s

(2012) conceptualization of probabilistic commitments to create a variable indicat-

ing whether an alliance agreement is deterministic. Our coding indicates whether

any agreement promising active military support allows escape through voluntary

or probabilistic reasons (Benson 2012). The reason for including this variable is sim-

ilar to the justification provided for including the renunciation conditions. An alli-

ance is considered deterministic if it commits members to military action for

either compellent or deterrent purposes without the option of escape. We also

include Benson’s (2011, 2012) coding of unconditional alliances. An alliance is con-

sidered unconditional if it commits members to military action for either compellent

or deterrent purposes without any conditions on casus foederis. It is reasonable to

expect that military obligations that do not allow for escape and do not impose con-

ditions on military involvement beyond specifying whether the objective is compel-

lence or deterrence likely bind members to a broader range of military circumstances

than those that impose conditions on military action or allow members to escape.

Measuring the Depth of Commitments

Many scholars agree that alliances also vary in the depth of the commitments

included in the agreement. That is, the content of formal alliances differs in the




degree to which the agreement contains formalized and binding commitments.3 Our

conception of the depth of an alliance commitment follows from the view that

alliance commitments themselves impose varying levels of costs on alliance mem-

bers beyond those associated with the risks of conflict. Such costs include sunk for-

mation costs (Fearon 1997; Smith 1995) and peacetime military coordination costs

(Morrow 1994; Snyder 1997). Deeper alliance agreements impose higher costs while

shallower commitments impose lower costs.

To estimate a single measure of depth, we use several existing variables of dif-

ferent provisions in alliance agreements that impose costs on alliance members.

Building on Leeds and Anac (2005), we include in our characterization of depth

several measures of provisions that formalize the imposition of peacetime costs

and that institutionalize certain aspects of a military alliance. Accordingly, we

include the following variables: military contact, common defense policy, inte-

grated command, military aid, military basing, specific contribution, organization,

economic aid, and secret. Military contact indicates whether the agreement

requires contact between the militaries of the alliance members during peacetime.

Common defense policy indicates whether alliance members are required to con-

duct a common defense policy including common doctrine, coordination of train-

ing and procurement, joint planning, and so on. Integrated command is a variable

that indicates whether alliance members are obligated to integrate military com-

mand among allies both in peacetime and in wartime. Military aid indicates

whether alliance members are required to provide unspecified military aid, grants

or loans, and/or military training or technology transfer. The variable military

basing captures whether the alliance agreement contains provisions stipulating that

members agree to jointly place troops in a neutral territory or station troops in a

members’ territory. Specific contribution indicates whether the agreement speci-

fies details about the contributions to be made by one or more of the allies or how

the costs of the alliance should be divided. Organization is a variable that specifies

whether the agreement requires members to create any stand-alone organizations

or other organizations that provide for regular meetings of government officials

or the named organization. Economic aid indicates whether the agreement includes

obligations for providing economic aid for nonspecific reasons, postwar recovery,

or for trade concessions. Secrecy is a variable that specifies whether alliances are

public, public but contain some secret provisions, or totally secret.

Measuring the Potential Military Capacity

Conventional approaches for measuring the potential joint military capacity of

an alliance include summing the capabilities of the alliance partners using the

Composite Index of National Capabilities (CINC scores; Singer, Bremer, and

Stuckey 1972). Accordingly, we include capabilities, which is the log of the

summed CINC scores of all alliance members. While aggregate capabilities pro-

vide one estimate of the raw potential military capability of the alliance, other




factors related to specific characteristics of the signatories might also enhance or

constrain the military capacity of the alliance. We also include major power, which

is a variable indicating whether at least one alliance member is a major power

(Correlates of War 2011). The presence of a major power in an alliance may affect

the overall military capacity of an alliance. Scholars claim that major powers pos-

sess unique characteristics that give such alliances a distinctive military advan-

tage—for example, they possess significantly greater economic resources, have

more economic and security interests, possess advanced weapons systems (such

as nuclear weapons in the post–World War II [WWII] era), and influence in inter-

national institutions such as the United Nations Security Council (Gibler and Vas-

quez 1998). Although scholars generally agree that major powers are qualitatively

distinct from other powers, measuring their impact on the military capacity of an

interstate alliance is not straightforward. Scholars typically use a separate indicator

to control for the presence of a major power (Levy 1981; Siverson and Tennefoss

1984; Morrow 1991; Leeds 2003a; Benson 2011).

The distance between alliance members is another factor that might influence the

overall potential military capacity of an alliance. In particular, the distance

between allies may degrade the signatories’ combined capabilities because of the

cost related to projecting military forces and coordinating long-distance military

actions (Boulding 1962; Starr and Most 1976; Bueno de Mesquita 1983; Bueno

de Mesquita and Lalman 1986; Smith 1996; Weidmann, Kuse, and Gleditsch

2010; Bennett and Stam 2000b). We include a variable for distance (Bennett and

Stam 2000a). Our measure includes the mean of all paired combinations of alliance

members.4 The distance to a target country may also be relevant for assessing

the strength of some alliances, but given the difficulty of identifying threats and

the aspiration to estimate the strength of alliances lacking a specified threat, we

omit this variable.5

Because the size of the alliance may also be a correlate of its military capacity,

we also include a measure for ally count, which is the log of the number of alliance

members according to ATOP (Leeds et al. 2002). Multiple signatories may provide

advantages in conflict bargaining, yield potential gains from division of labor and

specialization, and enhance the credible use of allies’ military capabilities beyond

the additive advantage of simply summing individual military capabilities. How-

ever, the relationship is somewhat unclear as more signatories may complicate

logistical coordination and increase the chances of that allies’ opinions and inter-

ests will diverge.

Finally, the commonality of security interests may affect the resolve of signa-

tories to contribute in a war. One common approach is to use ‘‘s-scores’’ to measure

of the closeness of foreign policy interests (Signorino and Ritter 1999) based on the

similarity of countries’ alliance portfolios. We include a measure for sglo, which we

calculate by taking the mean s-score of all paired combinations of alliance members.

Regime type may also affect signatories’ willingness to contribute in war. More

democratic alliances may or may not also produce stronger alliances. Democratic




allies may lead to common security interests, and domestic audience costs may lead

democratic alliances to be more credible (Lai and Reiter 2000; Leeds et al. 2002;

Gibler and Sarkees 2004; Mattes 2012). On the other hand, the relationship is not

entirely clear because democracies may prefer not to ally with one another (Simon

and Garzke 1996; Gibler and Wolford 2006) because the veto points created by

domestic political institutions may create difficulties for taking action (e.g., Tsebelis

2002) or because election-induced leadership turnover may make them unreliable

(Gartzke and Gleditsch 2004). We include a measure of how democratic, on average,

the signatories are. We calculate POLITY by taking the mean Polity IV score for all

alliance members (Marshall, Jaggers, and Gurr 2002).

A Statistical Measurement Model

The challenges scholars confront when characterizing the nature of military

alliances are endemic to the social sciences. How do we use several multiple obser-

vable features to estimate a parsimonious measure that summarizes the structure

of the common variation we observe? We know, for example, that an alliance

that commits the signatories to establish joint military bases, integrate military

commands, and provide economic and military aid is one that requires deep com-

mitments. How do we compare such an alliance with such provisions to an agree-

ment made in secret and which requires ongoing military contact and establishes a

formal organization? All of these aspects are related to the depth of the commit-

ment entailed by the alliance, but it is not clear which set of obligations imposes

greater costs. Similar difficulties arise when describing the scope of an alli-

ance—is an offensive alliance with specific conditions for its invocation broader

in scope than a unconditional and open-ended defensive pact? Even assessing the

potential military capacity of an alliance can pose difficulties when making com-

parisons—does an alliance between two major powers with very dissimilar alli-

ance portfolios have a greater military potential than an alliance among many

like-minded countries that are located in close proximity to one another?

Scholars currently have three unsatisfying options for resolving these measure-

ment issues. One possibility is to focus the analysis on a single proxy variable at

a time. This approach is problematic because it fails to account for the considerable

variation that may exist within the values of the chosen variable. For example, while

the terms of the average offensive alliance may obviously reflect broader commit-

ments than the terms of an average neutrality agreement, there may still be important

variation within alliance agreements that are categorized as offensive. For example,

the 1939 Pact of Steel alliance between Germany and Italy is widely viewed as an

example of an aggressive military alliance with sweeping terms. As offensive alli-

ances goes, it is indeed both expansive and relatively deep, obligating alliance mem-

bers to commit military support under both offensive and defensive circumstances as

well as establishing ‘‘standing committees’’ in both countries for the purpose of




remaining in constant military contact and consulting about actions to take if ‘‘the

common interests of the contracting parties [are] injured.’’

It may be difficult to imagine an offensive alliance requiring more of its mem-

bers than the Pact of Steel. There are examples of offensive alliances that are more

explicit in imposing specific costs. There are, as well, alliances that contain simi-

larly aggressive text but contain few to no costly provisions beyond the primary

offensive and defensive obligations. The 1941 WWII Axis agreement among

Germany, Italy, and Japan is an example of the latter category. It simply states that

‘‘Germany, Italy and Japan jointly and with every means at their disposal will pur-

sue the war forced upon them by the United States of America and Britain to a vic-

torious conclusion.’’ The content of agreement does not contain provisions that

impose additional costs such as joint military contact, military aid, basing, or inte-

grated military command. Of course, the agreement was signed during WWII, and

so it may make sense that the signatories would not specify peacetime costs in the

agreement and wartime costs may be implied by the phrasing of the primary obli-

gation: ‘‘with every means at their disposal will pursue the war . . . ’’ But a few

years later in 1944, the United Kingdom and Ethiopia also signed an offensive alli-

ance during WWII, which exceeded both the Pact of Steel and the WWII Axis in

the level of detail it used to specify the explicit obligation created by the alliance.

In addition to the primary offensive and defensive obligations, it also required sig-

natories to maintain official military contact in both wartime and peacetime; it sti-

pulates that the United Kingdom would organize, train, and administer the

Ethiopian army; and it allows for British basing in Ethiopia. This variation in the

depth of the agreement terms across these three ‘‘offensive’’ alliances underscores

the challenges associated with using a single coarse variable to proxy for concepts

with more subtle distinctions.

A second approach for accounting for the variation in alliances is to create an

additive index based on multiple characteristics. This method is problematic because

there is no theoretical guidance for combining the measures or interpreting the

resulting scale. Even if we think that the establishment of joint military bases, inte-

grated military commands, and the provision of economic and military aid signals a

deeper level of commitment between signatories than an alliance that lacks these

features, how do we evaluate the magnitude of the differences in the level of depth?

For example, is an alliance with two of these features twice as ‘‘deep’’ as an alliance

with only one? Moreover, how do we compare an alliance that commits signatories

to both economic and military aid to one that only provides for joint military bases

and an integrated military command? It seems difficult to rationalize the relation-

ships that are assumed by an additive index, and the assumed equivalences increase

as the number of variables used to construct the measure increases.

A third approach is to use a regression specification to predict the effect of some

features of an alliance on an outcome of interest y, while controlling for multiple

other features relevant to the concept in question. For example, if we are predicting

the effect of alliance scope, for example, on outcome y, the typical regression




specification y ¼ a þ b1x1 þ b2x2 allows the left-hand side to measure the scope of

an alliance—as a linear function of x1 and x2—and its relation to y.6 Including mul-

tiple measures in a regression changes measurement issues into specification issues.

Additionally, including a host of variables to account for variation in the nature of

alliances may also adversely affect the number of degrees of freedom that scholars

have, given the number of potential indicators of alliance strength. Interpreting the

effects from a saturated regression model can pose difficulties (Ray 2003; Achen

2005), particularly if the model includes multiple interactions (Braumoeller 2004;

Brambor, Clark, and Golder 2006).

If the question of interest relates to alliance formation—for example, what

accounts for the willingness of signatories to sign wide-ranging alliances rather than

more limited alliances—the regression approach provides no help. Scholars inter-

ested in such questions are forced to choose to focus on a particular measure

(e.g., Benson 2012) despite knowing that any single measure is an imperfect proxy.

Multiple regressions using multiply proxies may obviously be run, but there is no

simple way of providing a parsimonious assessment of the relationship of interest

in such circumstances. Moreover, a shortcoming of all of these approaches is that,

as indirect measures of a latent concept, they all fail to reflect our uncertainty about

how the observed concepts relate to the actual concepts of interest and to account for

the precision with which we are able to characterize such concepts.

In contrast to these three approaches, a Bayesian latent variable model provides a

principled framework for extracting concepts that are theoretically related to obser-

vable features of alliances using weaker assumptions than the alternatives noted

above. Non-Bayesian methods are certainly available, but for both theoretical (see

the arguments of Gill 2002 and Jackman 2009a) and practical reasons we adopt a

Bayesian approach. Most notably, unlike a frequentist approach, a Bayesian latent

variable approach allows us easily to quantify our uncertainty about the resulting

estimates using the posterior distributions of estimated parameters.

To focus our exposition, suppose we are interested in measuring the scope of alli-

ance obligations and let x�i denote the scope of alliance i at the time of its formation.

Even if we cannot know the actual scope, we can use characteristics of the agreement

that are theorized to be related to the scope of alliance i—for example, whether the

alliance is a commitment to offensive actions, whether there are specific conditions

placed on the commitment, and whether signatories are committed to military action

without the flexibility of escape—to estimate x�i . In so doing, we want to describe the

relative scope of various alliances and also quantify our level of uncertainty about

these characterizations. If we have k 2 1: : :K observable measures of a dimension

of interest, let the observed value for variable k for alliance i be denoted as xik.

Observed measures may include continuous (e.g., the average distance between signa-

tories), binary (e.g., whether a major power is involved), and ordinal measures.

The statistical measurement model we use to relate observable aspects to the

underlying dimension of interest is identical to that used to estimate how




democratic a country is or how liberal a district or a member of the US Congress is.

A Bayesian latent variable model provides a principled way of relating observed

features to a latent dimension that is thought to be responsible for generating the

association between the observed characteristics (see, e.g., Quinn 2004; Jackman

2009b). The idea is neither new nor controversial, and while these models have

been used to measure concepts critical for studying the politics of the United States

(e.g., Clinton and Lewis 2008; Levendusky and Pope 2010) and comparative pol-

itics (e.g., Rosenthal and Voeten 2007; Rosas 2009; Pemstein, Meserve, and Mel-

ton 2010; Treier and Jackman 2008; Hoyland, Moene, and Willumsen 2012),

scholars have only recently begun to apply the models to concepts in international

relations (see, e.g., Schnakenberg and Fariss 2014; Gray and Slapin 2011; Dur

et al. 2014).

Figure 1 provides a graphic representation for the three measures to provide an

intuition for the measurement model. As Figure 1 makes clear, the model assumes

that x�i is related to xi1, xi2, and xi3 across alliances, but it allows the relationship

to differ between variables. For example, xi1 and xi2 may be related to x�i in different

ways, and these differences are captured by b1, b2, s21, and s2

2.

Given the number of estimated parameters, estimating alliance characteristics

(x*) from the matrix of observed characteristics (x) requires additional structure. The

Figure 1. Directed Acyclic Graph: Bayesian latent variable model.

Note: Circles denote observed variables and squares denote parameters to be estimated.




Bayesian latent variable specification (see, e.g., Jackman 2009a, 2009b) we use

assumes that for all alliances:

xi � N bk0 þ bk1x�i ;s2k

� �: ð1Þ

The measurement model of equation (1) assumes that the observed correlates of

the alliance characteristic x are related to that characteristic in identical ways across

the N alliances but that different measures may be related to alliance strength in dif-

ferent ways. For example, the relationship between the scope of an alliance and

whether it entails offensive characteristics is identical across alliances—that is,

bk1 does not vary by i—but offensive objectives may be more related to the scope

of an alliance than whether there are specific provisions regarding the conditions

under which the agreement may be renounced by the signatories (i.e., bk1 may be

greater than bk2).

The model allows for differences in both the mean value of the observed measure

xk and the latent concept x* (as this will be reflected in the estimate of bk0), and it

also allows the scale of the observed and latent variables to differ (accounted for

by bk1). The β parameters therefore allow us to probe whether observed factors are

related to the underlying concept of interest—bk1 > 1 implies that a one-unit change

in the latent scale of x* corresponds to more than a one-unit change in the observed

measure xk, bk1 < 1 implies that a one-unit change in the latent scale corresponds to

less than a one-unit change in the observed measure, and bk1 < 0 implies that positive

values of xk correspond to negative values of x*. The model can also account for the

possibility that a measure is unrelated to the latent dimension, if bk1 ¼ 1. In addition

to the estimating the nature of the correlation between the observed and unobserved

variables, the s2k term allows for varying amounts of error in the precision of this

relationship. Finally, because we estimate a version of equation (1) for each of the

K observed measures, the relationship may vary across observed traits, and we can

use all available measures to help uncover the underlying latent trait.

These assumptions are silent about causality—nothing requires that the latent

trait x* causes the observed phenomena or vice versa. All that is assumed is that

there is a correlation between the observed and unobserved traits that can be used

to learn about the unobserved trait. For example, the Unified Democracy Scores

of Pemstein, Meserve, and Melton (2010) measure democracy using twelve expert

assessments even though the analyzed experts certainly do not cause democracy.

Similarly, Levendusky, Pope, and Jackman (2008) use various aspects of a congres-

sional district that are related to district ideology but which do not necessarily cause

it.

Given the unknown parameters x* and β to be estimated from the observed cov-

ariate matrix x, the likelihood function is:

L x�; βð Þ ¼ p xj x�; β½ �ð Þ / SNi¼1S

Kk¼1f

xi � bk0 þ bk1x�i� �

sk

� �; ð2Þ




where fð�Þ is the probability density function of the normal distribution. To com-

plete the specification and form the posterior distribution of x* and β, we assume

standard diffuse conjugate prior distributions.7

Given the discussion in the first section, we seek to characterize alliances

(x*) along three dimensions. Let x½1��i denote the potential military capacity

of the alliance (with estimates given by x½1�i), let x½2��i denote the depth of the

alliance commitments created by the provisions of the alliance (with estimates

x½2�i), and let x½3��i denote the scope of conditions falling under the purview

of the alliance (with estimates x½3�i). To identify the center of the latent space,

we innocuously assume that the means of x[1]*, x[2]*, and x[3]* are all 0. To

fix the scale of the recovered space, we assume that the variance of x*[1],

x*[2]*, and x*[3]* are also all 1. To fix the rotation of the space and define the

meaning of positive values, we assume that higher values of the summed capac-

ity of signatories correspond to positive values in the first dimension, alliances

that stipulate for joint military bases reflect a deeper and more costly commit-

ment for signatories, and compellent alliances receive positive values in the

third dimension.

We do not need to know the precise nature of the relationship between the

observed characteristics and the strength of the alliance to implement the model, but

we do need to identify which measures are, and are not, potentially related to each of

the three dimensions we are interested in. Following the discussion in the first sec-

tion, for every characteristic pertaining to either the depth or the scope of the com-

mitments created by the alliance, we assume that β[1]¼ 0; for any characteristic not

related to the depth of the alliance, we assume that β[2] ¼ 0; and for every charac-

teristic not related to the scope of the alliance, we assume that β[3] ¼ 0. That is, to

define the meaning of the dimensions we recover, we assume that only those mea-

sures that are thought to be theoretically related to the dimension influence the esti-

mated alliance score on that dimension.

Because we identify the latent dimensions by making assumptions about alli-

ance characteristics, our statistical measurement model can shed important

insights into the relationship between the these alliance characteristics and a

question we consider later is how alliance characteristics x*[1], x*[2], and

x*[3] are related.

Given these measures and identification constraints, we use the Bayesian latent

factor model that can accommodate both continuous and ordinal measures described

by Quinn (2004) and implemented via MCMCpack (Martin, Quinn, and Park 2011).

We use 100,000 estimates as ‘‘burn-in’’ to find the posterior distribution of the esti-

mated parameters, and we used one of our every 1,000 iterations of the subsequent

1,000,000 iterations to characterize the estimates’ posterior distribution. Parameter

convergence was assessed using the diagnostics implemented in CODA (Plummer

et al. 2006).




Estimates of Alliance Features

Our Bayesian latent variable model not only produces estimates about the scope of

the obligations, depth of the commitments, and the potential military capacity but

also reveals how the various observable features described in the first section are

related to each. Exploring these relationships helps assess the construct validity of

our measurement model.

Estimating three dimensions of alliance characteristics enables the inspection

of the relationship between alliances across dimensions to locate the estimated

alliance scores in the recovered space. We began this article by considering the

difficulty in making comparisons between alliances such as the 1920 Franco-

Belgian accord and the 1915 alliance between France, UK, Russia, and Italy.

Using our measures, we find that the 1915 alliance is among the most wide-

ranging alliance agreements with an estimated scope score of 2.40 (on a variable

that is assumed to have a mean of 0 and a standard deviation of 1). It was formed

during World War I, contained both offensive and defensive provisions, and did

not impose limiting conditions on alliance members’ use of military force to

achieve the war objective. Yet, with a depth score of only 0.225, it was not a deep

agreement in the sense that it did not formalize costly commitments regarding

military integration and coordination. In contrast, the content of the 1920

Franco-Belgian accord provided a depth score of 2.63 and a scope score of only

0.207. Accordingly, the terms of the 1920 agreement formalized many costly

commitments that the 1915 agreement lacked, but it was not nearly as sweeping

in terms of the circumstances under which alliance members’ were obligated to

use actual military force.

Figure 2 plots the distribution of alliance estimates in the dimensions of potential

military capacity (x - axis and the scope of the obligations contained in the alliance

agreement (y - axis). A score is estimated for each of the 489 alliances signed

between 1816 and 2000 for which we have data on the observable characteristics

(plotted in gray), but we focus our attention on a few selected alliances to illustrate

the face validity of our estimates. (The Online Appendix contains the full set of esti-

mates and standard errors, and it also contains an extensive discussion of alliances in

the World Wars and East Asia along those two dimensions.)

As Figure 1 shows, the most powerful alliance in terms of potential military

capacity is the Allied agreement in WWII. This alliance is a joint declaration

by 39 countries, including the United States, Russia, the United Kingdom, and

China. It is notably also one of the most sweeping agreements on the dimension

of scope. The terms of the agreement explicitly target Germany, Italy, and Japan

and contain no limiting conditions on the scope of alliance members’ military

obligations. It is a broad declaration of war in both offensive and defensive cir-

cumstances. The estimated location of this alliance is a reassuring starting point

for assessing the output of the estimates. We might expect that the winning alli-

ance in the world’s most widespread and deadliest war—one that included all of




the world’s major powers—is likely to contain some of the most aggressive obli-

gations and rank among the most militarily powerful alliances in history.

The estimate of other notable alliances further reflects reassuring differences in

Figure 1. Note the orientation of the 1958 United Arab Republic–Yemen (UAR) alli-

ance compared to the WWII Allied agreement. While the scope of the UAR contains

similarly broad military obligations, it does not have nearly same military might as

the WWII Allied agreement. The UAR agreement, which included Egypt, Syria, and

Yemen, was formed to unite the Arab community against the expansion of com-

munism in Syria and elsewhere in the Arab world (Walt 1987, 71-80). Gamal Abdel

Nassar, former president of Egypt and the president of the United Arab Republic,

insisted on a full union and control over both countries in exchange for his agree-

ment to use all offensive and defensive military capabilities to halt the rising influ-

ence of the Syrian Communist Party. Nassar then seized the control of Syria and

banned all political parties.

Even though the UAR alliance was weaker in terms of potential military capacity

than most other alliances in the data, it was sufficiently powerful to satisfy the

Potential Military Capacity

Sco

pe o

f Agr

eem

ent

−2 −1 0 1 2

−10

12

3

WWII Allies

US−Spain (1963)

Franco−Belgian Accord (1920)

U.A.E−Yemen (1958)

Belarus−Bulgaria (1993)

Figure 2. Potential Military Capacity and Scope of Alliance Agreements, 1815–2000.

Note: Points denote the posterior mean of the estimated alliance strength of each of the 489 allianceswe analyze. The ellipses denote the 95 percent regions of highest posterior density for the selectedalliances.




primary objective of the Union, which was to crack down on the Syrian Commu-

nists. It is noteworthy also that Jordan and Iraq formed the short-lived Iraq–Jordan

Federal Union at the same time. According to Walt (1987), the Federal Union was

designed to balance against the UAR.8 Our measure suggests that the estimates for

the potential military capacity of the UAR and Federal Union were indeed evenly

matched. In fact, our measurement model estimates that the UAR and Federal Union

are nearly indistinguishable on all three dimensions—scope, depth, and potential

military capacity.

In contrast to both the WWII Allies and the UAR, the 1963 US–Spain alliance is

relatively limited in scope. In 1963, both governments codified a formal defense

pact, which was an extension of their defensive obligations formed in the Madrid

Pact of 1953. This alliance was replaced by new bilateral alliances in 1970 when the

scope of military obligations was further limited by the inclusion of a consultation

provision and then again in 1976. In 1982, Spain officially joined North Atlantic

Treaty Organization (NATO). As depicted in Figure 2, the scope of the US–Spain

alliance is relatively limited even though the alliance was relatively strong in terms

of its potential military capacity. Not only does it not contain offensive provisions,

but it also provides flexibility and the potential for limiting military action on alli-

ance members’ primary obligation. The primary obligation states that ‘‘a threat to

either country, and to the joint facilities that each provides for the common defense,

would be a matter of common concern to both countries, and each country would

take such action as it may consider appropriate within the framework of its consti-

tutional processes.’’ This commitment is soft both on the amount of military support

to be provided and whether military action might even be guaranteed.

Also at the lower end of the scope dimension is the 1993 Belarus–Bulgaria agree-

ment. Although it is significantly less militarily powerful than the US–Spain alliance

and even though it is classified by ATOP as having no defensive or offensive

military obligations (in contrast to the US–Spain alliance which is classified as

defensive), the Belarus–Bulgaria accord, like the US–Spain agreement, is limited

in scope. The formal terms of the primary obligation state, ‘‘In case of a situation

which, according to one of the parties threatens its security or world peace, the par-

ties promise to hold immediate consultations on the measures of resolution of such a

situation.’’ While it is clear that the agreement aims at resolving security threats as

they arise, the agreement does not specify military obligations that members must

follow.

We now evaluate how notable alliances compare to one another when we relate

the potential military capacity of the signatories to the depth of the alliance agree-

ment. Figure 3 presents this relationship and reveals a clear and meaningful variation

in the alliances we observe along these two dimensions. First, consider again the

comparison between the WWII Allied agreement and 1958 UAR Union. Whereas

before we saw that the terms of these two agreements were similar in scope, the

depth of the two agreements differs significantly. The terms of the UAR agreement

called for the integration of the allies’ militaries, unified command over those forces,




and the full grant of military power and foreign policy authority to a unified com-

mand. By contrast, the Allied agreement contained no such terms.

Much of this difference is likely due to the fact that the Allied agreement was

signed in wartime, making the institutionalization of costly peacetime organizations

and military integration less relevant. However, the presence of war does not always

account for the lack of the depth of different agreements. As an illustration of this

point, note that the 1944 alliance between the United Kingdom and Ethiopia was

also signed during WWII. It is approximately equal to the WWII Allied agreement

in terms of scope (with a scope score of 2.51). Yet, even as a wartime agreement, it

ranks among the deepest agreements (with a depth score of 2.06), committing mem-

bers to expend costs to maintain military contact in both wartime and peacetime.

Additionally, the agreement specified that British must organize, train, and admin-

ister the Ethiopian army, while the Ethiopian government will cede certain of its ter-

ritory to be administered by the British military.

Another interesting comparison is the 1963 US-Spain alliance and the 1993

Belarus–Bulgaria accord. We saw that both alliances were at the low end of the

Potential Military Capacity

Dep

th o

f Agr

eem

ent

−2 −1 0 1 2

−10

12

3

WWII Allies

US−Spain (1963)

Franco−Belgian Accord (1920)

U.A.E−Yemen (1958)

Belarus−Bulgaria (1993)

Figure 3. Potential Military Capacity and Depth of Commitment, 1815–2000.

Note: Points denote the posterior mean of the estimated alliance strength of each of the 489 allianceswe analyze. The ellipses denote the 95 percent regions of highest posterior density for the selectedalliances.




scope dimension but significantly different from one another in terms of potential

military capacity. Figure 3 shows that they are different in terms of both depth and

military capacity. Whereas the Belarus–Bulgaria agreement includes no terms for

the expenditure of peacetime costs, the US–Spain alliance specifies that both mili-

taries will remain in contact and requires the US government to provide military

equipment as well as funding for Spain’s defense. Additionally, it calls for the for-

mation of a consultative committee between the two sides. In terms of the depth of

the commitment, the Belarus–Bulgaria agreement is much more similar to the WWII

Allied agreement, in spite of having fundamentally different military obligations,

than the US–Spain alliance is to the WWII Allied agreement, despite the fact that

both of these latter two alliances include the US as a signatory and, therefore, contain

significant potential military capacity.

Components of Alliance Dimensions

To validate our measure further it is instructive to compare how the various inputs

included in the model relate to the estimated dimensions. By doing so highlights the

following two advantages of our measurement approach: (1) our estimates reflect the

characteristics of multiple measures without having to specify the precise nature of

the relationship and (2) we can recover variation between alliances who possess the

same value for any particular measure because our measure does not necessarily

depend on a single measure (e.g., ‘‘offensive alliances’’). We are particularly inter-

ested in assessing the inputs of the dimensions of scope and depth, since these mea-

sures are truly novel.9

Figure 4 reveals that many aspects that are thought to be related to the depth of an

alliance commitment are related to the estimated dimension in expected ways. In

particular, the most prominent feature of an alliance with costly obligations is the

requirement for extending military aid and establishing military bases. These two

provisions are followed closely by maintaining military contact, establishment of

a formal organization, the specification of particular obligations, and an integrated

military command.

Terms of an alliance agreement that provide for economic aid and the secrecy of

the agreement have either little or no relationship to the depth of the obligations

specified by the alliance according to our measurement model. A feature of our mea-

surement model is that the variability in the relationship between these measures and

the underlying dimensions means that we can use these results to compare the depth

of alliance agreements containing different sets of obligations—an agreement spe-

cifying military aid and a integrated military command, for example, is estimated

to be associated with imposing a more costly commitment on signatories than an

agreement containing only stipulations for the exchange of economic aid and a com-

mon defense.

In terms of the scope of the alliance agreement, we again find reassuring correla-

tions between the measures we observe and the dimension we estimate. Figure 5




shows the factor loadings for the inputs included in the model estimation for the

scope of obligations. As expected, agreements that contain unconditional pledges

of offensive and compellent military support are all estimated to be more expansive

in scope than defensive agreements that condition military action on circumstances

related to the war environment such as a particular target or location. It is also reas-

suring that our measurement model predicts that the alliance with the most limited

scope would be a consultation or neutrality pact.

In sum, not only does our measurement model produce estimates of prominent

alliances that comport well with historical and qualitative investigations, but the alli-

ance characteristics that are thought to be theoretically related to each of the three

dimensions are also revealed to be related as expected. These examinations suggest

the validity of our approach and the resulting estimates.

Secrecy

Economic Aid

Common Defense

Integrated Command

Specific Oblig.

Organization

Military Contact

Military Bases

Military Aid

−0.5 0.0 0.5 1.0

−0.5 0.0 0.5 1.0

Figure 4. Factor Loadings: ‘‘Depth of Specified Obligations.’’

Note: Circles denote posterior mean and lines denote 95 percent HPD regions. HPD ¼ highest posteriordensity.




Construct Validity

Understanding the conditions under which various types of alliances are formed and

the decision of how broad and deep to design the terms of the agreement are impor-

tant questions for better understanding the way in which countries construct the

international arena through their choices of actions and our measures provide the

necessary characterization to begin these important investigations. In addition,

applying our measures in an applied analysis of alliance formation helps validate the

construct validity of our measures by showing that features that are theoretically

thought to be related to the formation of different alliance types are revealed to

be so using our measures.

Consultation Pact

Neutrality Pact

Non−mil. action reqd only if requested

Renunciation Prohibited

Renunciation Allowed

Renunciation Conditional

Mil. action depend on non−provoc.

Non−mil. action depend on war env.

Conditional (other)

Mil. Action depend on non−compliance

Defensive Pact

Mil. Action depend on war env.

Deterministic

Compellent

Offensive Pact

Unconditional

−0.5 0.0 0.5 1.0

−0.5 0.0 0.5 1.0

Figure 5. Factor Loadings: ‘‘Scope.’’

Note: Circles denote posterior mean and lines denote 95 percent HPD regions. HPD ¼ highest posteriordensity.




Scholars of alliances have theorized that different factors might be expected to

give rise to different alliances on the three dimensions that we estimate. Existing

work focuses on explaining variation in the observed measures—Benson (2012), for

example, disaggregates deterrent types of alliances and studies why differences exist

among these alliances—but we can use our measures to explore such question with

more confidence. In particular, we specify regression models that test whether fac-

tors identified by scholars of alliance formation are, as theorized, associated with

alliance formation as predicted. In particular, we estimate models of scope and depth

with robust standard errors where all measures are taken in the year that the military

alliance was formed.10 In each case, the goal is to use factors in the regressions that

have not already been used to construct the measures of scope and depth themselves.

In contrast to the measurement model that seeks to include aspects inherent to an

alliance that are thought to affect the underlying concept of interest, the goal in these

regressions is to evaluate whether the resulting estimates reflect theoretically

expected correlations in terms of aspects that are thought related to each concept but

that do not themselves comprise it.

We first estimate a model of the scope of the obligations in an alliance agree-

ment. Theories of alliance formation explain that concerns of entrapment create

incentives for alliance members to design agreements to include conditions that

limit military obligations and/or create flexible options for escape (Snyder 1984,

1997; Fearon 1997; Benson 2012). Benson’s (2012) theory of moral hazard and

alliance formulation predicts that alliance members’ design the content of alliance

agreements to be more flexible and to allow for probabilistic escape as alliance

members’ preferences and capabilities diverge (Benson 2012). However, empiri-

cal tests of this theoretical model are limited by the unavailability of a measure,

such as our estimate of scope, that captures continuous variation of limits on the

obligations that signatories include in the design of their agreements. Benson

(2012) uses a coarse ordinal measure of particular conditions and qualifications

included in alliance agreements.

Using estimates generated from our measurement model, we estimate a regres-

sion of the effects of divergent preferences and capabilities on the scope of an agree-

ment. Divergent preferences are measured using the average UN affinity scores

between pairs of alliance members, and difference in capabilities is measured by

subtracting the CINC scores of the strongest and weakest pair of alliance members.

We also include variables for the year in which the alliance was formed (start year

and start year2), because alliance agreements become noticeably more limited in

scope over time. Finally, we also include in the regression our measure of depth,

since it may be associated with scope.

Table 1 presents the results of model 1. Using our measure of scope, it is clear that

alliances agreements are designed to be more limited as signatories’ preferences and

capabilities diverge. The coefficients for divergent preferences and difference in

capabilities are both negative and significant. These results confirm our expectations

from theory and provide further reassurance that our measures correctly capture




valid and meaningful concepts. Additionally, our measure of depth is also positively

related to scope, though the effects are only significant at the p � .10 level.

It is important to note, however, that the finding on divergent capabilities only

holds after 1945. As shown in model 2, prior to 1945, not only does the result not

hold, it is actually positively associated with scope, suggesting that, at least for

some early time period, alliances were designed to be broader when members’ cap-

abilities were more divergent.11 It is possible that the advent of nuclear weapons

dramatically exacerbated concerns of moral hazard in the post-WWII era by sig-

nificantly widening the capabilities gap between nuclear and nonnuclear states and

significantly increasing the risks associated with being involved in a conflict.

Using our measure of scope, we have not only been able to evaluate an existing

theory of moral hazard and alliance formation but also identified an intriguing puz-

zle about different effects of the divergence of alliance members’ preferences on

agreement design that may raise new questions about moral hazard, military tech-

nology, and alliance formation.

In addition to estimating a model of scope, we regress depth on several covari-

ates that are predicted to be associated with the extent to which an agreement

imposes peacetime and formation costs on alliance members. Many scholars argue

that individual incentives for opportunism may lead to deeper agreements (Leeds

and Anac 2005; Abbott and Snidal 2000; Lake 1999). Prospective allies who have

divergent preferences may have greater incentives to behave opportunistically.

Snyder (1997, 11) claims that divergent preferences often lead states to include

Table 1. Regression of the Formation Conditions for the Scope and Depth of AllianceAgreements.

(1) (2) (3)Scope Scope Depth

post-1945 pre-1946 post-1945

Constant 1,417.91y (859.15) 361.70 (317.87) �2,747.45* (1,259.62)Divergent preferences

(UN score)�0.57** (0.14) 0.63* (0.30)

Difference in capabilities �1.15* (0.46) 3.24** (1.07)Depth 0.09y (0.05) 0.46** (0.14)Democracy 0.004 (0.17)Major power involved 0.57** (0.14)Avg. log(capacity) �9.61** (2.44)Scope 0.30* (.14)Start year �1.42 (0.87) –0.37 (0.34) 2.80* (1.27)Start year2 0.0004 (.0002) 0.0001 (.0001) �0.0007* (0.0003)N 267 189 267R2 .32 .21 .24

Standard errors in parentheses.Note: yp < .10, *p < .05, **p < .01.




costly actions in their alliance commitments to ‘‘validate’’ agreements ‘‘when

interests of allies are somewhat divergent, or when they are subject to change . . . ’’

According to Snyder, when signatories’ preferences diverge, ‘‘The partner will

need to be reassured that one’s underlying interests are not so at odds with the

contract that the alliance is no more than a ‘scrap of paper.’’’ Additionally, states

with divergent preferences may need to come to an agreement on how their mili-

taries will coordinate. Formalizing these terms in an alliance enhances the depth of

the commitment. Consequently, we use UN affinity scores to measure the diver-

gence of foreign policy preferences of alliance members in the year that the alli-

ance was formed.

Other factors, which also might create worries of opportunism, may lead alli-

ance members to design agreements with deep commitments. If major powers and

nondemocracies pay relatively lower costs for violating agreements (Leeds

2003a), then at the alliance formation stage such states may need to provide addi-

tional assurances to signal commitment (Fearon 1997; Morrow 1994). If so, then

when states with these attributes are party to an alliance, we might expect the terms

of the agreements to impose deeper costs as a signal of commitment. Lake (2011)

provides an additional explanation for why the presence of a major power might

increase the depth of an alliance agreement. According to Lake, dominant states

benefit from establishing rules that both discipline subordinates and credibly com-

mit to limit their own power. Accordingly, we might expect that alliance agree-

ments with major power allies will formalize treaty terms that establish security

organizations and impose military coordination costs on members. Thus, in

model 3, we include a variable for major power, which indicates whether at least

one major power is party to an alliance agreement at the time of signing. We also

include a variable for democracy, which is measured by creating an indicator for

each alliance member that is a democracy according to Polity IV (Marshall, Jag-

gers, and Gurr 2002) and then taking the average across all alliance members at

the time of formation.12

Another factor that may be associated with the depth of an agreement is the

military strength of the signatories. A primary advantage of military alliances is

the synergistic benefit that comes from realizing economics of scale through joint

military coordination (Lake 1996, 1999; Conybeare 1992, 1994). That is, deep mil-

itary coordination may expand alliance members’ joint capabilities beyond states’

additive raw capabilities. States with already relatively low capabilities may espe-

cially benefit from such coordination, and relatively stronger states may feel less of

a need to pay peacetime military costs to gain coordination benefits. We explore

this relationship by including a variable for the average log(capacity) of the alli-

ance using the members’ average CINC scores at the time of formation. Finally, we

also include our measure of scope as a variable, because we might expect that alli-

ances with broader scope of alliance obligations require, on average, costlier com-

mitments both to coordinate more extensive military obligations and to signal the

credibility of a broader range of commitments.13




As Table 1 reveals, all of these variables except for democracy are associated

with depth as expected. The result for divergent preferences is especially interesting,

given that the coefficient is positive when estimating depth. Recall that divergent

preferences were negatively related to scope in model 1. The opposite relationship

with these dimensions reassures us that the measures of scope and depth capture dis-

tinct concepts. In the regressions of both scope and depth that we have estimated in

this section, not only have the results added to our confidence that the measurement

model has recovered conceptually valid aspects of alliance variation from our mea-

surement model but also yielded substantively relevant findings about theoretically

meaningful predictions of the formation of formal military alliances.

Conclusion, Caveats, and Implications

Scholars of alliances have been blessed with a tremendous amount of data due to the

generous and impressive efforts of those who have collected data on both the formal

terms of the various alliances and the characteristics of the signatories involved. The

amount of available data prompts the question, How can we best measure the

strength of international alliances, given the wealth of available data and our theo-

retical conceptions of alliance strength while also accounting for the inevitable

ambiguity that must necessarily accompany such a determination?

We show how a Bayesian latent variable trait model—a model that has been

applied to many other important concepts in political science—can be used to inte-

grate observable measures with theoretical arguments about the determinants of

alliance strength to provide estimates of how the various observable factors relate

to the theoretically implied dimensions, how the strength of alliances in the two

dimensions relate to one another, and how certain we are about all of the estimated

parameters. Applying the model to all alliances in the international system

between 1816 and 2000 provides estimates of alliance strength in terms of the

strength of signatories and the strength of the formal terms of the alliance agree-

ment. We include alliances that are multilateral and lack a specific target. The esti-

mates have strong face validity—familiar alliances are located as we would

expect, and exploring the post-WWII alliances of East Asia provides reassuringly

reasonable estimates.

Not only do our estimates provide scholars with measures that can be used to

explore questions such as the determinants of alliance formation, they are also rel-

evant for other pressing topics in the study of military alliances such as the

persistence of alliances, their relationship with conflict, and their reliability.

Additionally, the estimates also reveal important insights into the nature of

alliances. For example, although there is a relationship between the depth and

scope of military agreements, the correlation is modest (.112), and there is con-

siderable variation of potential interest in the relationship. Moreover, when

comparing the estimates of temporally and geographically proximate alliances

involved in the World Wars and East Asia, the estimates suggest that many of the




alliances that are formed are nearly balanced. Perhaps reflecting the theoretical

claims of balance of power theorists (Morgenthau 1948; Waltz 1979), alliances

formed in response to one another are very similar in military capacity and often

bear similarities in the scope of the terms of the obligations. Third, the ability to

assess the certainty with which we are able to estimate the location of alliances

provides the ability to account for the precision of our estimates when comparing

alliances or using the estimates in secondary analyses. Finally, although we think

our estimates are theoretically sound and possess strong face validity, the mea-

surement model we employ is sufficiently general that scholars can use the model

to generate their own estimates using different assumptions or different measures.

Such flexibility in the applicability of the method may, for example, be of value if

scholars wish to evaluate questions that call for the examination of only active

military alliances or just those with specific targets.

We think our measure and the method provide an important advance for scho-

lars interested in alliances and the international system, but some caveats are worth

noting. First, while our statistical model provides a principled way of extracting

information from multiple measures related to theoretically relevant dimensions

with a minimal number of assumptions, the resulting estimates are still dependent

on the relationship between the observable measures to extract the latent dimen-

sions. For example, the fact that CINC scores are relative to the global capacity

in each year means that comparisons across long periods of time may be dif-

ficult and the estimates are likely most appropriate for temporally comparisons

or when temporally related differences are accounted for (similar concerns can

emerge whenever these scores are used in any regression that explores variation

over time).

Second, the ability to use a Bayesian latent variable model to extract the latent

dimensions structuring the strength of an alliance does not ameliorate potential con-

cerns about the endogeneity of alliances. While we have been careful not to include

input variables in the measure of our three dimensions of scope, depth, and potential

military capacity that scholars may seek to correlate in regressions of these same

measures, nothing in our analysis discounts the fact that the formation of an alliance

is presumably a strategic act based on the assessment of expected consequences, and

those interested in using the estimates should be careful of the potential pitfalls.

While no measure is perfect, our model is able to use theoretical insights to iden-

tify how features are related to the scope, depth, and potential military capacity of an

alliance in theoretically relevant dimensions. It also generates the measure for these

dimensions from observable characteristics of the signatories involved and the for-

mal terms of the agreement while also quantifying how certain we are about the

resulting estimates. Moreover, it also provides a principled way to integrate alterna-

tive measures and assumptions into the measurement task that produces estimates

that allow us to focus on better understanding the determinants and consequences

of alliances rather than continually having to grapple with the question of how best

to measure the variation across the alliances themselves.




Acknowledgment

The authors would like to thank Brett Ashley Leeds and Michaela Mattes for comments on an

earlier version of this manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research,

authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of

this article.

Supplemental Material

The online [appendices/data supplements/etc] are available at http://jcr.sagepub.com/

supplemental.

Notes

1. See Powell (1996) and Levy (1989) for a review of the debate over the relationship

between alliances, distribution of power, and stability.

2. The fifth section in the Online Appendix lists all of the factor inputs for each dimension

along with a description of the variable and its coding rule.

3. Scholars often refer to the depth of agreements and international institutions. For a review

of the literature regarding the formalization of cooperative security institutions and alli-

ances in particular, see Leeds and Anac (2005). Similar to our approach with military alli-

ance agreements, Dur et al. (2014) performs a factor analysis on 50 substantive provisions

to estimate the depth of preferential trade agreements.

4. Scholars have long recognized the need for adjusting aggregate military capacity for dis-

tance. Most existing research degrades strength linearly (see e.g., Bueno de Mesquita and

Lalman [1986] and Smith [1996]), but research has not established the actual mathemat-

ical relationship between distance and capabilities, and we also do not know if the rate of

degradation is sensitive to the technological sophistication and geography of a country.

Consequently, we make no assumptions about how distance degrades military capacity.

5. That said, scholars could certainly use our framework to estimate a more limited measure

for alliances with identified targets.

6. We can treat y ¼ aþ b1x1 þ b2x2 as accounting for the regression of y on the unobserved

alliance strength x*, given the true specification y ¼ a0 þ b0x� if we can assume that x*

is a linear function of x1 and x2. If, for example, x� ¼ g1x1 þ g2x2 and y ¼ a0 þ b0x�, the

regression of y ¼ aþ b1x1 þ b2x2 is equivalent to the regression of

y ¼ a0 þ b0 g1x1 þ g2x2ð Þ because a ¼ a0, b1 ¼ b0 � g1, and b2 ¼ b0 � g2 even though

we do not observe x*! Note, however, that this decomposition relies on the extremely

strong—and implausible—assumption that x� ¼ g1x1 þ g2x2. This requires that not only

must the latent trait be a function of observables that are correctly specified in the regres-

sion specification, but also that the relationship between x* and the observables is without




error. If there is error in this relationship—say x� ¼ g1x1 þ g2x2 þ e —then we are in a

classic error-in-variables situation and the estimated regression coefficients are inconsis-

tent (see, e.g., the nice review by Hausman 2001).

7. Specifically, the prior distribution of βk conditional on s2k is normally distributed and the

prior distribution for s2k is an inverse Gamma distribution (Jackman 2009a).

8. In the second section of the Online Appendix, we provide additional analysis of other

notable alliances that show further evidence of balancing based on our estimates.

9. Our measure of potential military capacity is a straightforward estimate of the combined

capabilities of the signatory states. It correlates highly with the summed CINC scores of

alliance members.

10. We also specify a regression of potential military capacity, which we include in section 4

of the Online Appendix.

11. Note models 1 and 3 include all alliances formed after data for United Nations affinity

scores is available in 1946. Model 2 does not include data for divergent preferences,

because the time period in this model is prior to the formation of the United Nations.

12. In other specifications, we also use other measures including average polity, a dummy

variable for at least one democracy, and the standard error of the mean polity score. None

of these measures has a significant effect on depth.

13. The effects of the other variables in the model are robust to the exclusion of scope.

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Assessing the Variation of Formal Military Alliances

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